What method have you been taught ?
Bisection, False Position, Fixed Point Iteration, Newton-Raphson ?
Here's a fast converging fixed point iteration, (though it's really Newton-Raphson).
x^3 + 2x = 90,
add 2x^3 to both sides,
3x^3 + 2x = 2x^3 + 90,
remove x as a factor on the lhs,
x(3x^2 + 2) = 2x^3 + 90,
divide,
x = (2x^3 + 90)/(3x^2 + 2).
Now, choose a starting value for x, substitute that into the rhs to calculate an updated value for x,
substitute that back into the rhs to update further, repeat as many times as you wish.
With a starting value of 4.5, the sequence is
4.5,
4.33865.
4.332706,
4.332698 etc.
(So it's 4.3 to 1dp.).
